Random Survival Forests With Competing Events: A Subdistribution-Based Imputation Approach

Abstract

Random survival forests (RSF) can be applied to many time-to-event research questions and are particularly useful in situations where the relationship between the independent variables and the event of interest is rather complex. However, in many clinical settings, the occurrence of the event of interest is affected by competing events, which means that a patient can experience an outcome other than the event of interest. Neglecting the competing event (i.e., regarding competing events as censoring) will typically result in biased estimates of the cumulative incidence function (CIF). A popular approach for competing events is Fine and Gray's subdistribution hazard model, which directly estimates the CIF by fitting a single-event model defined on a subdistribution timescale. Here, we integrate concepts from the subdistribution hazard modeling approach into the RSF. We develop several imputation strategies that use weights as in a discrete-time subdistribution hazard model to impute censoring times in cases where a competing event is observed. Our simulations show that the CIF is well estimated if the imputation already takes place outside the forest on the overall dataset. Especially in settings with a low rate of the event of interest or a high censoring rate, competing events must not be neglected, that is, treated as censoring. When applied to a real-world epidemiological dataset on chronic kidney disease, the imputation approach resulted in highly plausible predictor–response relationships and CIF estimates of renal events.